Topic

# Skew

About: Skew is a research topic. Over the lifetime, 8792 publications have been published within this topic receiving 98985 citations.

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TL;DR: In this paper, a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities.

Abstract: Summary. A fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is sufficiently general to encompass some recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew t-density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.

1,215 citations

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TL;DR: In this paper, a general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities.

Abstract: A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew $t$ density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.

1,174 citations

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01 Jan 1995

TL;DR: The document spectrum (or docstrum), which is a method for structural page layout analysis based on bottom-up, nearest-neighbor clustering of page components, yields an accurate measure of skew, within-line, and between-line spacings and locates text lines and text blocks.

Abstract: Page layout analysis is a document processing technique used to determine the format of a page. This paper describes the document spectrum (or docstrum), which is a method for structural page layout analysis based on bottom-up, nearest-neighbor clustering of page components. The method yields an accurate measure of skew, within-line, and between-line spacings and locates text lines and text blocks. It is advantageous over many other methods in three main ways: independence from skew angle, independence from different text spacings, and the ability to process local regions of different text orientations within the same image. Results of the method shown for several different page formats and for randomly oriented subpages on the same image illustrate the versatility of the method. We also discuss the differences, advantages, and disadvantages of the docstrum with respect to other lay-out methods. >

628 citations

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01 Jul 1977567 citations

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02 Sep 2013TL;DR: The findings suggest that skew is a critical factor in evaluating performance metrics and to avoid or minimize skew-biased estimates of performance, it is recommended to report skew-normalized scores along with the obtained ones.

Abstract: Recognizing facial action units (AUs) is important for situation analysis and automated video annotation. Previous work has emphasized face tracking and registration and the choice of features classifiers. Relatively neglected is the effect of imbalanced data for action unit detection. While the machine learning community has become aware of the problem of skewed data for training classifiers, little attention has been paid to how skew may bias performance metrics. To address this question, we conducted experiments using both simulated classifiers and three major databases that differ in size, type of FACS coding, and degree of skew. We evaluated influence of skew on both threshold metrics (Accuracy, F-score, Cohen's kappa, and Krippendorf's alpha) and rank metrics (area under the receiver operating characteristic (ROC) curve and precision-recall curve). With exception of area under the ROC curve, all were attenuated by skewed distributions, in many cases, dramatically so. While ROC was unaffected by skew, precision-recall curves suggest that ROC may mask poor performance. Our findings suggest that skew is a critical factor in evaluating performance metrics. To avoid or minimize skew-biased estimates of performance, we recommend reporting skew-normalized scores along with the obtained ones.

566 citations